Mathematical, Numerical and Experimental Study of Solitary Waves

The note discusses the motion of solitary waves on the free surface of a layer of water. The rigorous results for the existence of solitary-wave solutions of exact governing equations are given. To generate such surface waves, a moving bump placed at the bottom or a pressure source on the free surface is used. A model equation, called forced Korteweg-de Vries (FKdV) equation, is numerically studied and multisolitary-wave solutions are obtained. Then, the numerical solutions are compared with experimental results using a water tank with a moving bump at the bottom.